Line Spectrum Estimation and Detection with Few-bit ADCs: Theoretical Analysis and Generalized NOMP Algorithm

TL;DR

This paper analyzes the effects of low-bit quantization on line spectral estimation and detection, providing a theoretical framework and proposing a novel super-resolution algorithm, GNOMP, validated through simulations and real radar data.

Contribution

It introduces a comprehensive analysis of SNR loss in low-bit ADCs for spectral estimation and proposes GNOMP, a low-complexity super-resolution algorithm with CFAR capabilities.

Findings

Theoretical SNR loss bounds are established for low-bit quantization.

GNOMP outperforms existing algorithms in detection probability and resolution.

Validation with real mmWave radar data confirms practical effectiveness.

Abstract

As radar systems will be equipped with thousands of antenna elements and wide bandwidth, the associated costs and power consumption become exceedingly high, and a potential solution is to adopt low-resolution quantization technology, which not only reduces data storage needs but also lowers power and hardware costs. This paper focuses on line spectral estimation and detection (LSE\&D) with few-bit ADCs (typically 1-4 bits) by investigating the signal-to-noise ratio (SNR) loss, establishing a framework to understand the impact of intersinusoidal interference, the bit-depth of the quantizer, and the noise variance on weak signal detection in scenarios involving multiple sinusoids under low-resolution quantization. Additionally, a low-complexity, super-resolution, and constant false alarm rate (CFAR) algorithm, named generalized Newtonized orthogonal matching pursuit (GNOMP), is proposed. Extensive numerical simulations are conducted to validate the theoretical findings, particularly in terms of the detection probability bound. The effectiveness of GNOMP is demonstrated through comparisons with state-of-the-art algorithms, the Cram\'{e}r Rao bound, and the detection probability bound. Real data acquired by mmWave radar further substantiates the effectiveness of GNOMP in practical applications.